To find the perimeter of a triangle with vertices of (1,2), (3,−4) and (−4,5), we have to first find distance between each pair of points, which will give length of sides. For this we use distance formula between two points (x_1,y_1) and (x_2,y_2) is sqrt((x_2-x_1)^2+(y_2-y_1)^2). Hence if lengths of sides are L_1,L_2,L_3, these are as follows:
L_1=sqrt((3-1)^2+((-4)-(2))^2)=sqrt(2^2+(-6)^2)=sqrt(4+36)=sqrt40=2sqrt10=6.325
L_2=sqrt((-4-(3))^2+(5-(-4))^2)=sqrt((-7)^2+9^2)=sqrt(49+81)=sqrt130=11.402
L_3=sqrt((-4-1)^2+(5-2)^2)=sqrt((-5)^2+3^2)=sqrt(25+9)=sqrt34=5.831
Hence Perimeter is 6.325+11.402+5.831=23.558
